Differential cross section measurements of top quark pair production for variables of the dineutrino system with the CMS experiment

Differential top quark pair cross sections are measured in the dilepton final state as a function of kinematic variables associated to the dineutrino system. The measurements are performed making use of the Run 2 dataset collected by the CMS experiment at the CERN LHC collider, corresponding to proton-proton collisions recorded at center of mass energy of 13 TeV and an integrated luminosity of 138 fb$^{-1}$. The measured cross sections are found in agreement with theory predictions and Monte Carlo simulations of standard model processes.

💡 Research Summary

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The CMS Collaboration presents the first differential measurement of top‑quark‑pair (t t̄) production that directly probes the kinematics of the invisible dileptonic neutrino system. Using the full Run 2 data set collected at √s = 13 TeV (integrated luminosity 138 fb⁻¹), the analysis selects events with two opposite‑sign leptons (e or μ), at least two jets (≥ 1 b‑tagged), and applies a veto on additional leptons. This selection yields a sample with ≈ 78 % signal purity, the dominant backgrounds being t t̄ + X, single‑top, and Drell‑Yan + jets.

Two observables are studied: the transverse momentum of the combined neutrino system (pₙₙᵀ) and the minimum azimuthal separation between the reconstructed missing transverse momentum vector (𝑝⃗ₜ^miss) and each lepton, denoted Δφₘᵢₙ. These variables are motivated by beyond‑the‑Standard‑Model (BSM) scenarios that introduce extra invisible particles (e.g. stop‑pair production with neutralinos), where the shape of the pₙₙᵀ and Δφₘᵢₙ spectra can differ from the SM expectation.

A central technical achievement of the work is the improvement of the missing‑transverse‑momentum (MET) resolution through a dedicated deep neural network (DNN) regression. The DNN, a fully‑connected feed‑forward network with two output nodes (the x and y components of the MET correction), is trained on simulated events to predict the difference between the PUPPI‑based reconstructed MET and the true generator‑level MET. Input features include jet and lepton kinematics, event‑level quantities, and the number of primary vertices. After regression, the MET magnitude resolution improves by ~15 % and the azimuthal resolution by ~12 % relative to the uncorrected PUPPI MET. This enhancement reduces bin‑to‑bin migrations in the unfolding step, allowing finer binning and smaller systematic uncertainties.

Systematic uncertainties are evaluated separately for experimental and theoretical sources. Experimentally, the jet‑energy‑scale (JES) dominates across most bins, followed by b‑tagging efficiency, lepton reconstruction, and luminosity. Theoretical uncertainties are assessed by varying renormalisation/factorisation scales, matrix‑element–parton‑shower (ME‑PS) matching, the choice of tW‑t t̄ overlap removal scheme (diagram‑subtraction vs diagram‑removal), colour‑reconnection models, and background normalisations. The impact of these variations is propagated through the response matrix used in the regularised unfolding.

To demonstrate sensitivity to possible BSM contributions, a closure test is performed with a stop‑pair signal (𝑚̃ₜ = 525 GeV, 𝑚̃_χ⁰ = 350 GeV) added to the SM prediction and scaled by a factor of ten. The test uses three unfolding strategies – regularised matrix inversion, a regularised version with smoothing, and a simple bin‑by‑bin correction. All three methods successfully recover the injected BSM shape in the two‑dimensional (pₙₙᵀ, Δφₘᵢₙ) distribution, confirming that the analysis framework can detect sizable deviations from the SM.

The measured differential cross sections are presented both as one‑dimensional spectra in pₙₙᵀ and Δφₘᵢₙ and as a two‑dimensional distribution. They are compared to five theoretical predictions: POWHEG+PYTHIA8, POWHEG+HERWIG7, MC@NLO+PYTHIA8, a fixed‑order NLO calculation, and a NNLO QCD calculation for leptonic observables. Overall, the data agree with all predictions within uncertainties. Small shape differences are observed, most notably in the highest Δφₘᵢₙ bin, echoing previously reported discrepancies in the lepton‑lepton azimuthal angle distribution. These residual differences may hint at higher‑order effects or modelling aspects that merit further study.

In summary, this work establishes that differential measurements based on the invisible dileptonic neutrino system are feasible and can be performed with high precision when MET reconstruction is enhanced by machine‑learning techniques. The results provide a new benchmark for SM top‑quark modelling, improve the experimental toolkit for future BSM searches involving missing energy, and set the stage for even more precise studies with upcoming high‑luminosity LHC data.